Reaction Chemistry & Engineering

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conditions, membranes, and reactors for efficient hydrogen production from ammonia

Item Type Article

Authors Realpe, Natalia;Kulkarni, Shekhar Rajabhau;Cerrillo, Jose Luis;Morlanes, Natalia Sanchez;Lezcano, Gontzal;Katikaneni, Sai P.;Paglieri, Stephen N.;Rakib, Mohammad;Solami,

Bandar;Gascon, Jorge;Castaño, Pedro

Citation Realpe, N., Kulkarni, S. R., Cerrillo, J. L., Morlanés, N., Lezcano, G., Katikaneni, S. P., Paglieri, S. N., Rakib, M., Solami, B., Gascon, J., & Castaño, P. (2023). Modeling-aided coupling of catalysts, conditions, membranes, and reactors for efficient hydrogen production from ammonia. Reaction Chemistry & Engineering.

https://doi.org/10.1039/d2re00408a Eprint version Publisher's Version/PDF

DOI 10.1039/d2re00408a

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Chemistry &

Engineering

PAPER

Cite this: DOI:10.1039/d2re00408a

Received 29th September 2022, Accepted 2nd February 2023 DOI: 10.1039/d2re00408a rsc.li/reaction-engineering

Modeling-aided coupling of catalysts, conditions, membranes, and reactors for efficient hydrogen production from ammonia †

Natalia Realpe, âShekhar R. Kulkarni, âJose L. Cerrillo, âNatalia Morlanés, â Gontzal Lezcano, âSai P. Katikaneni, ^bStephen N. Paglieri,^bMohammad Rakib,^b Bandar Solami,^bJorge Gascon âcand Pedro Castaño *âc

The production of high-purity, pressurized hydrogen from ammonia decomposition in a membrane catalytic reactor is a feasible technology. However, because of the multiple coupled parameters involved in the design of this technology, there are extensive opportunities for its intensification. We investigated the coupling between the type of catalyst, process conditions, type of membrane, and reactor operation (isothermal and non-isothermal) in the catalytic decomposition of ammonia. First, we developed an agnostic dimensionless model and calculated the kinetic parameters for a set of lab-made Ru- and Co- based catalysts and the permeation parameters of a Pd–Au membrane. The non-isothermal model for the Pd–Au membrane reactor was validated with the experiments using Co-based catalysts. Finally, we analyzed the coupling conditions based on the model predictions, results obtained in the literature and our experimental results, including several case studies. The thorough analysis led us to identify optimized combinations of catalyst–conditions–membrane–reactor that yield similar or improved results compared to the ones of Ru-based catalyst in a non-membrane reactor. Our results indicate that optimizing a single factor, such as the catalyst, may not lead to the desired outcome and a more holistic approach is necessary to produce pressurized and pure hydrogen efficiently.

1. Introduction

Hydrogen is assuming a leading role in the upcoming energy- fuel scenario owing to its emission-free combustion.¹ However, it suffers from inherent transportation and storage challenges that limit the potential benefits of its widespread, large-scale implementation as a fuel.² Hydrogen vectors or carriers do not require the transport or storage of large quantities of on-site hydrogen.³ These hydrogen-containing vectors can be organic or inorganic molecules that can be easily converted to pure hydrogen with ease and exhibit a minimal carbon footprint.⁴Ammonia stands out compared to multiple hydrogen vectors primarily owing to its high

volumetric-energetic density, low liquefaction pressure of ca.

8 bar, and a global production and distribution network.^5–7 Ammonia decomposition is an endothermic reaction that is thermodynamically favored at low pressures.⁸ However, pressurized hydrogen production is desirable to decrease costs and derived emissions of its post-production compression for its storage and transportation⁹(ca.6.0 kW h kg⁻¹ for compression of H2 to 70 MPa, which leads to approximately 1.3 kg of CO2 kg⁻¹ of H2).¹⁰ The energy analysis in our previous work¹¹allowed us to prove that the efficiency of the whole process (including the post- compression stage up to 350 bar) would drop from 77.7% to

∼68–73%, when hydrogen in the permeate is produced at 1– 20 bar, respectively, thus highlighting the significance of developing reliable kinetic models at high pressure.

Many active phase–support combinations have been studied in the literature with Ru-based catalysts as the benchmark with remarkable activities at low temperatures.^12,13 In addition, multiple non-noble metals, such as Fe, Co, and Ni, have been tested for this reaction,^14–17 albeit displaying lower activities at low temperatures in contrast to Ru-based catalysts. In addition to the development of new catalysts, the use of a catalytic packed bed membrane reactor (denoted hereafter as a membrane

aKAUST Catalysis Center (KCC), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia.

E-mail: [email protected]

bCarbon Management R&D Division, Research and Development Center, Saudi Aramco, Dhahran 31311, Saudi Arabia

cChemical Engineering Program, Physical Science and Engineering (PSE) Division, King Abdullah University of Science and Technology, Saudi Arabia

†Electronic supplementary information (ESI) available. See DOI:https://doi.org/

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reactor) has been proposed as an intensification route facilitating the production of high-yield and high-purity hydrogen.^18–20 For a given catalyst, the comparison of the membrane reactor against the catalytic packed bed reactor (denoted hereafter as a non-membrane reactor) typically leads to improvements in the conversion and a relatively pure hydrogen stream.²¹

The modeling of membrane reactors is tackled by solving fundamental equations of mass balance, transport phenomena, and chemical kinetics in a standard shell-tube geometry.^22–24 Hydrogen permeation via the membrane, driven by the pressure difference between the retentate and permeate sides, has been represented either as a linear pressure difference dependence²¹or as the Sieverts–Fick law considering the permeation to be proportional to the difference of the square root of retentate and permeate pressures.²⁵ Moreover, hydrogen permeance through the membrane is considered to be temperature-dependent and thereby expressed in the form of Arrhenius law.^26–28Pd-based materials have been extensively studied as hydrogen selective layers,^29–40 although other additional novel materials have been reported, some of which have remarkable hydrogen permeances and selectivities.^41–57Most modeling studies are performed for the benchmark Ru-based catalysts, and the kinetics are often represented with the Temkin–Pyzhev model or modifications thereof on account of its simplicity or to express the decomposition kinetics mathematically, thus resulting in an expression with a positive order ammonia and a negative order hydrogen dependence of varying magnitudes.^58–66 The hydrogen reaction order significantly varies from catalyst to catalyst in the range of−2.5 to−0.25; it is commonly regarded as negative. Thus, maintaining a low partial pressure of hydrogen is beneficial for reaction kinetics in the membrane reactor.

Two dimensionless numbers are used to identify the underlying governing mechanisms in the operation of membrane reactors, namely, the Damköhler (Da) and Peclet (Pe) numbers. Using these numbers allows the operation to be separated into several zones, each of which is defined by the associated limiting factors: kinetics, convection, and permeation. The relatively high endothermicity of ammonia decomposition poses challenges to the isothermal operation, particularly for larger reactors.^22,67 In this non-isothermal scenario, the Stanton (St) number is employed to create a dimensionless assessment of the energy balance⁶⁸ and measures how far the reactor operates from the isothermal condition.

Gómez-Garcíaet al.⁶⁹modeled an Fe-catalyzed membrane reactor (high-pressure retentate stream, atmospheric pressure on the permeate side, and with a sweep-gas) and identified four operation zones that are either kinetically or permeation controlled. Furthermore, they compared the relative improvements to equilibrium conversions under various operating conditions. Li et al.²¹ performed ammonia decomposition in a membrane reactor using a sweep gas through a concerted experimental and dimensionless

simulation approach. Using Da and the permeation number (the equivalent of Pe), they demonstrated how hydrogen yields and purity could be tuned for silica-based and Pd- based membranes. The former includes permeation selectivitiesαNH₃/H₂andαN₂/H₂, accounting for the slip of NH3

and N2across the membrane, thereby reducing the purity of separated H2for membranes with low selectivity.

Our study focuses on developing an agnostic model in terms of the catalyst, process conditions (temperatures between 350 and 600°C and pressures from 1 bar to 20 bar), membrane properties, and reactor operation (membrane and non-membrane, or isothermal and non-isothermal) for identify coupling and intensification possibilities between these parameters for the decomposition of ammonia in a catalytic membrane reactor. To validate the developed model, we performed a number of experimental tests in (i) an isothermal catalytic packed-bed reactor using Ru–K/CaO and Co–Ba/CeO2 catalysts, (ii) a Pd–Au/Al2O3 membrane module without a catalyst, and (iii) a non-isothermal catalytic packed- bed membrane reactor with the same Co-based catalyst and membrane. This builds on our recently published promising results¹¹ and expands to other experimental conditions, catalysts, and non-isothermal reactors. The data were used to estimate our lab-scale configuration's kinetic and permeation parameters and embed them within the model. Finally, we use the model and data published in the literature to establish the areas of optimization, coupling, and intensification.

Accordingly, we discuss how this holistic model can be used.

2. Methodology

2.1 Reactor model statement

We consider the geometry and conditions of a shell-tube catalytic packed bed membrane reactor (Fig. 1) to derive the numerical model. The porous tube inside is covered by a selective layer allowing H2permeation. The catalyst is placed in the shell side, thus forming a packed bed in the annular

Fig. 1 Schematic and sectional view of the catalytic packed bed membrane reactor used for ammonia decomposition.

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space. The feed enters at the top of the reactor, and the generated H2 permeates through the selective layer towards its center across the reactor length. Assuming a co-current operation of the reactor, permeated H2 exits at the bottom.

The remaining gases (N2 and unreacted NH3, if any) flow down the catalytic bed (retentate side).

A pseudo-homogeneous one-dimensional mathematical model is chosen to describe the system, assuming that axial diffusion of mass and heat and radial concentration gradients on both sides are negligible. Based on the experimental observations, the kinetic control regime was proven due to the absence of external and internal mass and heat transfer limitations for all simulated operating conditions. The procedure used to prove that all experiments were obtained under kinetic control is described in the ESI†document of our previous work.⁷⁰Other assumptions of the model are: (i) steady- state operation, (ii) plug flow in both feed and permeate streams, (iii) co-current operation, (iv) no concentration polarization effect through the membrane, and (v) isothermal operation on the permeate side. Under these assumptions, the following material balance equations are obtained in the axial (z) direction for the three species involved:

dFi

dz ¼νirrxn

AcWcat

V

−J_iAm

L ð ÞPxi ⁿ−Ppy_in

(1)

dQ_i dz ¼J_iAm

L ð ÞPxi ⁿ−Ppy_in

(2) whereF_iandQ_iare the molar flow rate of componentiin the catalytic bed and permeate side, respectively. Their corresponding mole fractions are designated asx_iand y_i.zis the axial direction along the reactor, A_cand Vare the cross- sectional areas and total volume of the bed, respectively,W_catis the total catalyst mass in the bed,A_m/Lis the membrane area per unit length of the reactor,PandP_pare the catalytic bed and permeate side pressures respectively, andr_rxnis the ammonia decomposition reaction rate. For NH₃and N₂, the permeation ordernis set to one, while for H₂0.5<n<1 depending on the phenomenon governing the permeation of H₂ across the membrane. J_i is the permeance of component i, and its temperature dependence is expressed using the Arrhenius expression.

J_i¼J_i;0exp −Ea;J

RT

(3) Both energy and momentum balances corresponding to the catalytic bed section are similar derived based on a one- dimensional steady-state plug flow model. Eqn (4) is the energy balance of the catalyst bed:

dT

dz¼ 1

P^N^s

i¼1FiCp;i νirrxn

AcWcat

V

−ΔHrxn

ð Þ þAcAsU V ðTw−TÞ

(4) where T is the temperature of the catalytic bed, Cp,i is the specific heat of component i, As is the reactor-oven contact

surface, U is the overall heat transfer coefficient between the catalytic bed and the reactor wall, and Tw is the reactor wall temperature. The total momentum balance to the catalytic bed section is as follows:

dP dz¼− G

ρdp

1−ϕ ð Þ

ϕ³

150 1ð −ϕÞμ

dp þ1:75G

(5) where G is the superficial mass velocity of the gas, ϕ is the catalytic bed porosity,d_pis the average catalyst particle diameter, μ is the viscosity, andρis the density of the gas. Catalytic bed porosity is assumed to be 0.55 and the particles are assumed to be well-rounded spheres with a diameter of 500μm.

2.2 Kinetics of ammonia decomposition

In the literature, the Temkin–Pyzhev equation (eqn (6)) has been used to describe the ammonia decomposition reaction rate.^58–65This rate law represents a modification of a power law considering the effects of proximity to the equilibrium where nitrogen desorption is assumed as the rate- determining step. Note that the temperature dependence is expressedviathe two-term Arrhenius equation.

rrxn¼k0exp −Ea

RT

p_NH₃² p_H₂³

!β

− p_N₂ Keq2

p_H₂³ p_NH₃²

!1−β

0

@

1 A (6)

where k₀ is the pre-exponential factor, E_a is the activation energy, R is the universal gas constant, p_i is the partial pressure of component i, K_eq is the thermodynamic equilibrium constant, andβis the Temkin–Pyzhev empirical constant that correlates NH₃ and H₂orders of reaction with their stoichiometric coefficients. Other authors, including this work, successfully fitted both orders of the reaction independently (eqn (7)) and reported them over a wide range of pressures and temperatures. This is the case of Ru-based⁷⁰ and Co-based catalysts.^71,72

rrxn¼k0exp −Ea

RT

p_NH₃^ap_H₂^b 1− 1 Keq2

p_N₂p_H₂³ p_NH₃²

!! (7)

where a and b are the reaction orders of NH₃ and H₂, respectively. The equilibrium constant is computed from eqn (8), and ΔG°rxnis estimated with the correlation in eqn (9), valid for the 673–1273 K range.⁷³

Keq¼Y^N^s

i¼1

p_i=P° νi

¼exp −ΔG°rxn

RT

(8)

ΔG°rxn¼95 117−193:67T−0:035293T²þ9:22×10⁻⁶T³ (9) The activity of the catalyst is assumed to be constant due to lack of deactivation proven in our long-term stability tests.

No deactivation for at least 100 h was observed for the Ru- based catalyst.⁷⁴ As for the Co-based catalyst stability tests were carried out in the packed bed membrane reactor for over 600 h with no evidence of detrimental effects on ammonia conversion, hydrogen recovery, composition, or flow rates of the permeate and retentate.¹¹

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Table 1 Dimensionless variables, numbers, and parameters used in the model development

Dimensionless variables Dimensionless numbers Dimensionless parameters

f_i¼ Fi

FNH3;0 (10) Da¼k0exp−_RT^E^a

P^ðaþbÞ_f Wcat

FNH3;0 (15) αH2=i¼J_H₂

J_i (19)

q_i¼ Q_i

FNH3;0 (11) DaIII¼Da −ΔH_rxn

CpNH₃;0T0

(16) Pr¼Pf

P_p (20)

P̂¼P Pf

(12) Pe¼ FNH3;0

J_H₂AmPfn (17) Ĉ_p;i¼ Cpi

C_pNH

3;0 (21)

θ¼ T

T₀ (13) St¼ UAsTw

C_pNH

3;0F_NH₃_;0T₀ (18)

ζ¼z L (14)

Table 2 Dimensionless mass, energy, and pressure drop equations

Dimensionless equations Mass balances

df_i

dζ ¼νiDaxNH3 axH2

b 1− P_f Keq

x_N₂x_H₂³ xNH32

− 1 Pe

xin−y_iⁿ=Prn

αH2=i (22)

dq_i dζ ¼ 1

Pe

xin−y_iⁿ=Prn

αH2=i (23)

Energy balance

dθ

dζ¼DaIIIxNH3 axH2

b 1−K^Peq^f x_N2x_H2³

x_NH3²

þSt 1ð −θT0=TwÞ P^N^s

i¼1 f_iĈp;i

(24)

Momentum balance

dP

d̂ζ¼LGð1−ϕÞ²

Pfϕ²dp2 ½150þ1:75 Re (25)

Initial conditions Mass balances

f_i_ζ¼0¼ F_i;0 F_NH₃_;0 (26)

q_i|ζ=0= 0 (27) Energy balance

θ|ζ=0= 1 (28) Momentum balance

Pˆ|ζ=0= 1 (29) Open Access Article. Published on 02 February 2023. Downloaded on 3/5/2023 6:21:35 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.

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2.3 Dimensionless model

To evaluate the reactor performance in a wide range of operational conditions unconstrained by the reactor dimensions, a non-dimensional analysis of the mass, energy, and momentum balances was performed. This dimensional model is used to assess the system behaviorviadimensionless variables and numbers summarized in Table 1.

Four dimensionless numbers are defined: the (i) Damköhler number (Da), comparing the rate of reaction with the rate of convective mass transfer. Da can be increased by increasing the space–timeviaeither a high catalyst load or a low NH3 feed flow; (ii) third Damköhler number (DaIII), defined as the ratio of the heat absorbed in the reaction to the convective rate of heat supplied by the feed; (iii) Peclet number (Pe), indicating the correlation between the convective and diffusive mass transports in the catalytic bed.

A low Pe represents faster H2 permeation across the membrane, achieved by decreasing NH3 molar flow or increasing the driving force or the membrane area; and (iv) Stanton number (St) defined as the ratio between the heat externally transferred to the gaseous reaction medium and the energy content of the reaction medium. Higher St values indicate closeness to the isothermal operation.

Dimensionless forms of eqn (1)–(5) are obtained incorporating eqn (10)–(21).

Equations reported in Table 2 were simultaneously solved using inbuilt MATLAB solvers. Stiffness while integrating the initial reaction rates at small lengths arises from the negative H2 reaction order (absent in the feed). Therefore, an infinitesimal concentration of H2 (ca.

10⁻¹⁶) was defined in the feed for the simulation studies.²¹ The same approach was followed in determining the initial conditions for the permeate side wherein a small amount of an external inert component was assumed.

Fractional NH3 conversion and H2 recovery are defined as follows:

XNH3¼fNH3;0−fNH3;L−q_NH₃_;L

fNH3;0 (30)

RH2¼ q_H₂_;L fH2;Lþq_H₂_;L

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2.4 Experiments and fitting

In our previous studies, we investigated the ammonia decomposition reaction with two catalysts, Ru–K/CaO and Co–Ba/CeO2.^11,70,74 The Co-based catalyst with 80/20 molar Co/Ce ratio was synthesized by the co-precipitation method, followed by the addition of Ba (0.5 wt% Ba) as a promoter using the incipient wetness impregnation method. Ru–K/CaO was prepared using the impregnation method, followed by a pyrolysis step and final incorporation of potassium using the same method (10 wt% K). More details about synthesis, optimization and characterization of both catalysts can be found in our previous studies.^70,74 Herein, we expanded the

experimental database of both catalysts with additional experiments classified into three sets:

i. In an isothermal catalytic packed-bed reactor (Fig. S1 and S2†) using Ru–K/CaO or Co–Ba/CeO2catalysts, to obtain a dataset of 95 experimental data points for each catalyst under the following conditions: temperatures from 250 to 550 °C, pressures from 1 to 40 bar, space times from 0.2 to 6 gcath mol⁻¹, partial pressures of NH3from 0.05 to 1 bar, and partial pressures of H2 from 0 to 0.75 bar. The aim is to use the obtainedXNH₃to estimatek0,Ea,a, andbfor each catalyst.

ii. In an isothermal membrane reactor module (Fig. S3†) using a Pd–Au/Al2O3membrane, without a catalyst, to obtain a dataset of 55 experimental data points for different operating temperatures (350–500 °C), inlet flow rates (100– 4000 N mL min⁻¹), and feed pressures (4–9 bar). The aim is to useRH₂to estimateJ0andEa,J.

iii. In a non-isothermal catalytic packed-bed membrane reactor (Fig. S4†) using the Co–Ba/CeO2 catalyst, to obtain a dataset of 56 experimental data points under the following conditions: temperatures from 250 to 500 °C, space times from 2.6 to 40 gcath mol⁻¹, and feed pressures from 4 to 16 bar.

Parameters estimated with sets (i) and (ii) were incorporated in the mass balances (eqn (22) and (23)) and solved together with the energy balance to match experimental XNH₃ and RH₂, thus estimating the empirical heat transfer coefficient Uof the lab-scale setup (set (iii)).Tw

measurements were obtained at five points along the reactor for each experiment (Fig. S5†). A parabolic correlation (eqn (32)) was reported to determine the temperature profile along the reactor wall, in addition to a correlation (eqn (33)) to predict the inlet reactor temperature from the setpoint value (TwSP). Hence, unless the T0/Tw ratio is specified, eqn (32) and (33) determineT0andTwfromTwSP.

Tw=−100.57z²+ 95.77z+Tw_SP−22 (32) T0= 0.9Tw_SP+ 28 (33) where Tw, TwSP, and T0 are the reactor wall temperature, reactor wall setpoint temperature, and feed temperature at the reactor inlet, expressed in K.

Insights into the characteristics of experimental reactors used for new data acquisition of each set are available in the ESI.† Parameter estimation for each fitting set was achieved with the fminsearch function of MATLAB, employed to determine the minimum of unconstrained multivariable systems using a derivative-free method. The sum of the squared residuals (SSR) of the experimental data and predicted values (i.e., target variables likeXNH₃andRH₂) was set as the objective function to minimize (eqn (34)). The 95%

confidence intervals for nonlinear least squares parameter estimates were reported using the nlparci MATLAB function given the residuals and the Jacobian matrix at the solution. Error variance was computed from the SSR as per eqn (35).

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SSR¼X^N

i¼1

χ^exp−χ^cal 2

(34)

σ¼ ffiffiffiffiffiffiffiffiffiffiffi

SSR N−2 r

(35)

3. Results and discussion

3.1 Agnostic model results

The model developed up to section 2.3, which is agnostic in terms of catalyst, conditions, and membrane, is used to identify the regimes of potential coupling possibilities based on the understanding of which phenomena governs different operation regions. For this purpose, we investigate the influence of dimensionless numbers (Da, Pe, St) on the process performance, determined byXNH3andRH2.

Fig. 2 shows contour plots of NH3 conversion and H2

recovery for a representative catalyst, a= 0.5 and b= −0.75, using different Da and Pe values assuming a highly selective membrane to H2 (αH2/NH3 = 10⁵; αH2/N2 = 10⁵) operating at isothermal conditions. Fig. 2(a) can be divided into three regions: (i) the region comprising high Pe values (Pe> 10⁰) where NH3 conversion is independent of Pe, and the maximum conversion achieved is slightly >90%; (ii) the region bounded by 10⁻²<Pe<10⁰where the effect of the Pe is most noticeable and conversion of 100% is possible; and (iii) the region with Pe<10⁻²where conversion is practically unaffected by the Pe and Da values. For all regions identified in Fig. 2, the Da value positively affects the NH3conversion.

Based on its definition, the Da number (Table 1) can be

increased in many ways, e.g., by increasing the catalyst activity (temperature, pressure, and type of catalyst) or amount of catalyst (or space–time). The primary difference between region (i) and the other two is that the convective flow is higher than the permeation term. This region is not affected by Pe numbers because of the high convective flow, poor performance of the membrane, or its absence, thus approaching the behavior of a conventional packed bed (non- membrane) reactor. Therefore, maximum conversion in this region is limited by thermodynamic equilibrium. In region (iii), the effect of Pe on NH3 conversion is insignificant because of the limited membrane performance enhancement restricted by the maximum achievable driving force (i.e., H2

partial pressure in the catalytic bed) for permeation. In this region, the reactor performance is strictly controlled by reaction kinetics over permeation. Unlike other regions, in region (ii), conversion can be effectively tuned by modifying Da or Pe, the latter by increasing operating temperature, feed pressure, membrane area, or working with a more permeable material. For this study, this region represents an intensified area of interest. Therefore, these values of Pe and Da are used as a reference for upcoming simulations. The same regions are observed in Fig. 2(b). H2recovery is null for region (i) as it is only significant for cases where the H2

diffusive flux is significantly higher than the convective one.

As for region (ii), H2recovery is considerably influenced by a change in Pe, thus representing a regime controlled by the membrane characteristics. Region (iii) is affected only by the kinetics. These remarks agree with the previous observations.

For non-isothermal conditions, we examined the effects of different degrees of isothermal character on the reactor by assuming different values of St for Pe0 = 0.05 (membrane reactor) and Pe0= 500 (non-membrane reactor),Tw/T0= 1, and activation energies of 100 and 25 kJ mol⁻¹for a representative catalyst and membrane, respectively. Because certain dimensionless numbers vary along the reactor (e.g., Da with non-isothermal operation), the subscript 0 (e.g., Da0) is used to indicate its values at the reactor inlet. Fig. 3(a) shows that there is a maximum difference of 87% between the membrane reactor conversion at St = 0 (adiabatic) and St =∞(isothermal) at Da0 ≈1. This Da value is the minimum value required to achieve complete conversion in an isothermal membrane reactor. At extremely low Da values (Da0 < 10⁻²), conversions are limited, thus making the effect of St negligible. Fig. 3 shows that St = 100 is close to isothermal operation for the entire Da range. At a sufficiently high Da, the closer the operation is to an isothermal reaction, the larger the difference is between the conversion achieved in both reactors.

Furthermore, Fig. 3(a) shows that a membrane reactor not only can go beyond the intrinsic thermodynamic limitations of the reaction, but it also performs better than the non- membrane reactor under less isothermal scenarios (low-St operation). For values of St < 100, the Da requirements for achieving high NH3conversion exponentially increase. At Da0

< 0.1, all curves demonstrate the same conversion for the Fig. 2 Effect of Damköhler (Da) and Peclet (Pe) numbers on (a) NH3

conversion and (b) H2recovery. Simulation conditions: St =∞;Pr= 4;

Pp= 1 bar;Tw= 400°C;T0/Tw= 1;αH₂/NH₃= 10⁵;αH₂/N₂= 10⁵;a= 0.5;

b=−0.75;n= 0.5.Xeq@400°C= 99.8%.

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membrane reactor and the packed bed reactor. Fig. 3(b) shows dimensionless temperature profiles for Da0 = 1 and shows the similarity between St = 100 and the isothermal operation, where the feed temperature can be restored after the initial drop characteristic of endothermicity in this reaction. However, the initial temperature drop at lower St is more significant and cannot be neglected. Higher temperature drops in the membrane reactor compared to the non-membrane reactor are explained by higher heat consumption of the reaction (higher conversion) and heat loss of hydrogen permeating to the other side of the membrane.

Returning to the isothermal membrane reactor conditions, pressurized H2 production is explored by comparing the performance of a membrane reactor at different permeate pressures as a function of the feed and pressure ratio (Fig. 4). Fig. 4(a) shows the expected adverse effect of pressure for both the non-membrane reactor (dashed line) and equilibrium (dotted line) conversions.

Feed pressure negatively affects the thermodynamic equilibrium and kinetics. These effects are superposed by the positive impact on H2 permeation by increasing the driving force across the membrane, enhancing the net ammonia decomposition rate. However, there is a tradeoff between the desired permeate pressure and feed pressure required to obtain complete NH3 conversion (Fig. 4(a)). For example, a 3 bar feed pressure is required to completely

convert NH3to yield pure H2at 1 bar on the permeate side, whereas if an H2 product pressure of 15 bar is desired, all of the feedstock cannot be converted even at 100 bar.

When representing the former in terms of the pressure ratio rather than feed pressure (Fig. 4(b)), we observe that the pressure ratio required to reach 100% conversion becomes increasingly higher with the permeate pressure. Therefore, as per the model, high-pressure H2 production with complete feedstock conversion becomes asymptotically more pressure demanding as the desired product pressure increases up to the point where 15 bar H2 production would require a feed pressure of>150 bar. However, this seems not to be the case with the pressure ratio (ca. Pr= 1.5–2) required to overcome the non-membrane reactor performance, which is approximately Pr = 2 irrespective of the permeate pressure, and therefore setting the minimum pressure ratio for a membrane reactor. Fig. 4(c) and (d) show the same effect on H2 recovery. The similarity between the impact of different permeate pressures on H2 recovery determines that the minimum pressure ratio to achieve maximum recovery is∼Pr

= 6, virtually independent of permeate pressure. These observations agree with the experimental results reported in our previous study.¹¹The potential areas for the performance improvement are summarized in Table 3. Note that the values identified for Da correspond to the entire evaluated range in Fig. 2, indicating that tunning Da allows achieving any target conversion for a specific membrane reactor configuration.

In all previous simulations, the dimensionless form of the momentum balance (eqn (25)) was used to compute the pressure drop along the catalytic bed. None of the simulated conditions exhibited significant pressure drop values (<1%).

Hence, the pressure drop can be considered negligible for all operating Da, Pe, and St ranges addressed in this study.

Fig. 4 Permeate pressure effect on NH3conversion for different (a) feed pressures (Pf) and (b) pressure ratios (Pr); H2recovery for different (c) feed pressures (Pf) and (d) pressure ratios (Pr). Simulation conditions: Da/Pf(a+b)

= 1; Pe×Pfn= 0.05; St =∞;Tw= 400°C;T0/Tw

= 1;αH₂/NH₃= 10⁵;αH₂/N₂= 10⁵;a= 0.5;b=−0.75.

Fig. 3 St effect on (a) NH₃conversion as a function of the Damköhler number at the reactor inlet (Da₀) and (b) dimensionless temperature profiles,θ, for a membrane reactor (solid lines) and a non-membrane reactor (dashed lines) across the dimensionless length. Simulation conditions: Da₀= 1; Pe₀= 0.05 (membrane reactor); Pe₀= 500 (non- membrane reactor);Pr= 4;Pp= 1 bar;Tw= 400°C;T0/Tw= 1;αH₂/NH₃

= 10⁵;αH₂/N₂= 10⁵;a= 0.5;b=−0.75;n= 0.5;Ea= 100 kJ mol⁻¹;Ea,J= 25 kJ mol⁻¹;Xeq@400°C= 99.8%.

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Hence, additional references to the pressure drop are omitted when discussing these operating conditions. To support this observation, pressure drop estimations are shown in Fig. S6,† even for the most severe scenarios (i.e., 1000 N mL min⁻¹ NH3in the feed).

3.2 Parameter estimation

Kinetic parameters of Ru–K/CaO and Co–Ba/CeO₂ catalysts (set i), Pd–Au/Al₂O₃ membrane parameters (set ii), and the membrane reactor heat transfer coefficient (set iii) were estimated based on the previously described extended experimental sets. Fig. 5 shows the parity plots comparing the experimental and calculated target variables for all experimental conditions and parameter sets: (a) the kinetic model for the Ru–K/CaO and Co–Ba/CeO₂catalysts developed with experimental set (i), using NH₃ conversion as a fitting parameter; (b) the permeation model of the Pd–Au/Al₂O₃ membrane using experimental data from set (ii) with H₂ recovery as a fitting parameter; and (c) and (d) the non- isothermal membrane reactor model, experimental set (iii), using both NH₃ conversion and H₂ recovery, respectively.

Because of the relatively good fitting of all models, we claim that the set of assumptions is adequate for this system,i.e., eqn (7) is a reliable kinetic model for the ammonia decomposition kinetics in the evaluated ranges of operational

conditions for both catalysts and eqn (3) is adequate for modeling the H2permeation and the diabatic thermal regime is well represented by a curved wall temperature profile. The statistics for the estimated parameters in Table 4 likewise demonstrate the reliability of the fitting procedure.

Table 4 summarizes the estimated parameters for different experimental datasets. The modified Temkin– Pyzhev parameters obtained for Ru–K/CaO and Co–Ba/CeO2

catalysts show substantial differences, with the former showing faster overall kinetics with larger NH₃ and smaller H2reaction orders. The lowerEavalue estimated for the Co– Ba/CeO₂ catalyst indicates that the kinetic constant is less affected by the temperature than the Ru–K/CaO catalyst.

However, the fact that the pre-exponential factor of Ru–K/

CaO is one order of magnitude larger than that of Co–Ba/

CeO₂ agrees with the a priori expected higher activity of the former. The following section provides a full assessment of the estimated reaction orders and activation energies in the context of the previously reported values.

As per the membrane parameters, the fitted JH₂,0 and Ea,J

values lie within the range expected for H₂ selective Pd membranes, as shown in section 3.3. The estimated H₂ permeation order is in the lower limit of the acceptable values (n= 0.5). Because only H₂was detected at the permeate side in

Fig. 5 Comparison of experimental values and simulation predictions after parameter estimation of (a) set (i) (Ru–K/CaO, black squares: Co– Ba/CeO2, red circles); (b) set (ii); and (c) and (d) set (iii) in terms of NH3

conversion and H2recovery, respectively.

Table 4 Estimated parameters for different experimental datasets Parameter set i

Catalyst Ru–K/CaO Co–Ba/CeO₂

k₀(mol g⁻¹h⁻¹) (6.27 ± 0.01)×10¹¹ (3.33 ± 0.29)×10¹⁰ E_a(kJ mol⁻¹) 166.4 ± 0.1 154.1 ± 3.2

a 0.47 ± 0.00 0.37 ± 0.02

b −1.42 ± 0.00 −1.04 ± 0.02

r² 0.968 0.984

σ² 0.096 0.070

Parameter set ii

J₀(mol m⁻²s⁻¹Pa⁻ⁿ) (7.85 ± 0.11)×10⁻⁵

E_a,J(kJ mol⁻¹) 6.7 ± 1.6

n 0.5

αH2/N2 ∞

αH2/NH3 ∞

r² 0.991

σ² 0.040

Parameter set iii

U(W m⁻²K⁻¹) 244 ± 53

r² 0.945

σ² 0.057

Table 3 Identified ranges of interest for different dimensionless numbers and studied parameters

Dimensionless number/parameter Criterion Value

Pe Potential area for coupling 10⁻²<Pe<10⁰

Da Tune reactor performance under specific conditions 10⁻¹<Da<10⁰

St Avoid severe axial temperature gradients St>100

Pr Overcome non-membrane reactor performance Pr>2

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permeation-exclusive experiments (set (ii)) and membrane reactor experiments (set (iii)),αH₂/N₂andαH₂/NH₃were set to∞. Furthermore, experimental Pe0(0.03–0.61) and Da0 (0–20) are within the ranges defined in Table 3, indicating that the fitted parameters are suitable for the reactor–catalyst coupling study presented in the following sections. The value of the overall heat transfer coefficient at the wall, along with the dimensions of the reactor, corresponds to experimental values of 300<St0

< 1600, which based on our previous discussion, are sufficiently high values (St>100) to rule out significant heat- related limitations. These high values of St arise not only from the estimated value ofU, which is within the expected range based on the literature,^75–77 but also due to the annular geometry of the reactor.

3.3 Effect of model parameters

Once the model is fitted to our experimental results, it can be used (along with other experimental results available in the literature) to confirm the realistic coupling regions of the membrane reactor. Considering the effect of membrane properties, in Fig. 6(a) and (b), the impact of H₂/NH₃ membrane selectivity is shown for a wide range of H₂ permeances, representing a region 5×10⁻³< Pe < 5× 10³.

Herein, the results show that NH3 conversion forJH₂< 10⁻⁷ mol s⁻¹m²Pa^0.5is<90% and independent ofαH₂/NH₃, which for the FNH₃,0/Am ratio and selected Pr represents Pe > 10⁰, indicating that the H2 permeation flux is not sufficient to overcome non-membrane reactor performance. For higherJH₂

values and low H2/NH3 selectivity (αH₂/NH₃ < 10²), NH3

conversion (based on eqn (30)) can be lower than that obtained in a non-membrane reactor because of NH3

permeation. With the values ofJH₂>10⁻⁵mol s⁻¹ m⁻²Pa^−0.5 andαH₂/NH₃>10³, the complete conversion of ammonia can be achieved in the reactor. MinimumαH₂/NH₃requirements to achieve H2 purity higher than 99.9% are very similar. For most lab-scale studies reported for ammonia decomposition in a Pd-coated membrane reactor, αH₂/NH₃ is not reported because no NH3 is detected in the permeate side,22,24,25,78

indicating that although there is a minimum requirement of αH₂/NH₃on the order of 10³, in most of the reported cases this value is easily achieved for common H2 permselective materials. This is the case of the membrane studied in this work, for which pure H2 is obtained in the permeate in all experiments.

Fig. 6(c) shows the effect of H2/N2membrane selectivity on H2 purity. The most significant difference between Fig. 6(b) and (c) is the area bounded byJH₂>10⁵mol s⁻¹m⁻²

Fig. 6 Membrane properties' influence on membrane reactor performance, expressed as the effect of H2/NH3 selectivity (αH₂/NH₃) and H2

permeance (JH₂) on (a) simulated NH3conversion and (b) simulated H2purity (yH₂); H2/N2selectivity (αH₂/N₂) and H2permeance (JH₂) on (c) simulated H2purity (yH₂), and (d) their reported values in the literature; activation energy (Ea) and H2permeation order (n) on (e) simulated NH3

conversion and (f) their reported values in the literature. Simulation conditions: Da0= 1;FNH₃,0/Am= 0.1 mol m⁻²s⁻¹; St = 100;Pr= 4;Pp= 1 bar;

Tw= 400°C;T0/Tw= 1;αH₂/NH₃= 10⁵;αH₂/N₂= 10⁵;a= 0.5;b=−0.75;n= 0.5;Ea= 100 kJ mol⁻¹;Ea,J= 25 kJ mol⁻¹. For case (e),JH₂,0= 10⁻⁴mol m⁻²s⁻¹Pa⁻¹.Xeq@400°C= 99.8%.

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Pa^−0.5andαH₂/N₂<10², where H2/N2membrane selectivity has a more significant impact on H2 purity. In this region, permeance for NH3 and N2 is the same; however, as NH3 is converted along the axial position of the reactor, the partial pressure of the former decreases as opposed to the latter, directly affecting the permeation flux. Because of the N2 flux increases with NH3 conversion, H2/N2 membrane selectivity has a more significant effect on H2 purity than αH₂/NH₃. Fig. 6(d) shows the reported values of JH₂ and αH₂/N₂ for H2

selective materials tested in membranes. As per the model, most Pd/Al2O3 membranes are expected to yield a pure permeate. However, when using supports for Pd that endow extremely high H2permeation rates (e.g., PSS), the selectivity is compromised, and consequently so is H2 purity. The latter highlights the benefits of selecting membranes like Pd/Al2O3

that exhibit an excellentJH₂–αH₂/N₂balance. The estimated value ofJH₂at 400 °C for the Pd–Au/Al2O3 membrane used in this study (Table 4) is coherent with the values obtained for most Pd/Al2O3membranes and others that are exclusively selective to H2. Furthermore, considering values of αH₂/NH₃andαH₂/N₂on the order of 10³, for aJH₂on the order of 10⁻⁵as representative of an acceptable membrane performance for the simulation conditions, only Pd-based membranes meet the requirements.

In the simulations, the effect ofαH₂/N₂on NH3conversion was reported to be negligible and is not shown in Fig. 6.

Fig. 6(e) and (f) show the effects of the membrane permeation order, activation energy, and experimental values. Several reported H2 selective materials follow Sieverts–Fick's law (n= 0.5), indicating that the limiting step of H2 transport across the membrane is the diffusion in the film. However, other studies report deviations from this law (n > 0.5), indicating that the limiting step is the dissociation in the film or the transport across the porous support.⁷⁹ Based on the experimental data gathered in Fig. 6(f), a direct correlation between the membrane support and value ofn seems to be missing, highlighting that other factors in addition to the layer material and support (e.g., preparation method) certainly play a role. Under the simulated conditions, n does significantly contribute to the final performance. The activation energy has a more significant impact with a reduction of NH3 conversion of 10% when Ea,J increases from 10 to 25 kJ mol⁻¹. However, theEa,J value estimated in this work (6.7 kJ mol⁻¹) is similar to the Pd/Al2O3membranes in Fig. 6(f), which indicates that their performance is not highly influenced by the temperature. When the pre-exponential factor for permeance is sufficiently high, low activation energy membranes are preferred over higher ones as cold spot formation cannot be avoided nearby the reactor inlet where the reaction rates are the highest.

To explore the effect of catalyst kinetics on both reactor performances, the effects of activation energy (Fig. 7) and reaction orders (Fig. 8) were analyzed. In this simulation, we assumed the same pre-exponential constant (k0= 10¹¹mol h⁻¹ gcat−1) provided that a one-to-one comparison of the values reported in the literature is challenging because different

authors define the rate constant based on other terms.

However, considering our results of Ru- and Co-based catalysts, there is one order of magnitude difference between them (Table 4). This indicates that the effect of the pre-exponential constant must not be decoupled from the analysis in Fig. 7.

The theoretical impact of k0 andEa shown in Fig. S7† is as expected, namely, higherk0values allow complete conversions even if Ea is high. Despite the latter, the simulations and experimental results in Fig. 7 enable the comparison between different catalytic systems on the same basis and assess the impact of catalyst activity (Ea) on the reactor performance and wall temperature. In this manner, Fig. 7 shows that NH3

conversion is less dependent on reactor wall temperature for a membrane reactor than for a non-membrane reactor. The activation energy band dividing the reactive zone from the inactive area for a non-membrane reactor (125< Ea< 175 kJ mol⁻¹) is narrower and displaced to the right for the membrane reactor (137<Ea<185 kJ mol⁻¹), similar to what is observed in Fig. S7.†The simulations predict that for the assumed k0, Co–Ba/CeO2catalysts withEa= 154 kJ mol⁻¹(Table 4) achieve complete NH3 conversion at Tw > 420 °C in a membrane reactor; however, conversion in a non-membrane reactor using the same catalyst will not achieve complete conversion even at Tw = 500 °C. The role of Ea is highlighted with Fe-based catalysts, known to require higher temperatures along with higherEavalues.

Reaction orders play a central role in the selection of coupling strategies. In Fig. 8, we explore the effect of parameters a and b on the performance of a non-

Fig. 7 Contour plots for NH3 conversion for different reactor wall temperatures (Tw) and catalyst activation energies (Ea) for (a) non- membrane and (b) membrane reactors. Values reported in the literature are at scale. Simulation conditions: Pe0= 0.05 (membrane reactor); Pe0= 500 (non-membrane reactor);W/F0= 22 gcath mol⁻¹; St = 100;Pr= 10;Pp= 1 bar;T0/Tw= 1;αH₂/NH₃= 10⁵;αH₂/N₂= 10⁵;a= 0.5;b=−0.75;n= 0.5;k0= 10¹¹mol h⁻¹gcat−1;Ea,J= 25 kJ mol⁻¹. Open Access Article. Published on 02 February 2023. Downloaded on 3/5/2023 6:21:35 AM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence.